Random cascades of Gaussian scale mixtures and their use in modeling images with application to denoising

M J Wainwright, E P Simoncelli and Alan S Willsky.

Published in Proc 7th IEEE Int'l Conf on Image Proc (ICIP), vol.I pp. 260--263, Sep 2000.
© IEEE Computer Society

DOI: 10.1109/ICIP.2000.900944

This paper has been superseded by:
Random cascades on wavelet trees and their use in analyzing and modeling natural images
M J Wainwright, E P Simoncelli and A S Willsky.
Applied and Computational Harmonic Analysis, vol.11(1), pp. 89--123, Jul 2001.


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    • The detail coefficients of orthonormal wavelets applied to natural images are approximately uncorrelated. Despite this, they are by no means independent, but exhibit a strong self-reinforcing characteristic in that if one wavelet coefficient is large in absolute value, then "nearby" coefficients (where nearness is measured in scale, position, or orientation) also are more likely to be large in absolute value. We have developed a class of non-Gaussian multiscale processes, defined by random coarse-to-fine cascades on trees of multiresolution coefficients, that exhibit precisely these types of behavior. These cascades reproduce a rich semi-parametric class of random variables known as Gaussian scale mixtures (GSM). We demonstrate that this model class not only captures natural image statistics, but also facilitates efficient and optimal processing, which we illustrate by application to image denoising.
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